9.1 Find the following values for a lump sum assuming annual compounding:
a. The future value of $500 invested at 8 percent for one year
b. The future value of $500 invested at 8 percent for five years
c. The present value of $500 to be received in one year when the opportunity cost rate is 8 percent
d. The present value of $500 to be received in Five years when the opportunity cost rate is 8 percent
9.2 Repeat Problem 9.1 above, but assume the following compounding conditions:
a. Semiannual
b. Quarterly
9.7 Consider another uneven cash flow stream:
Year Cash Flow
0 $2,000
1 2,000
2 0
3 1,500
4 2,500
5 4,000
a. What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent?
b. What is the value of the cash flow stream at the end of Year 5 if the cash flows are invested in an account that pays 10 percent annually?
c. What cash flow today (Year 0), in lieu of the $2,000 cash flow, would be needed to accumulate $20,000 at the end of Year 5? (Assume
that the cash flows for Years 1 through 5 remain the same.)
d. Time value analysis involves either discounting or compounding cash flows. Many healthcare financial management decisions,
such as bond refunding, capital investment, and lease versus buy, involve discounting projected future cash flows. What factors must
executives consider when choosing a discount rate to apply to forecasted cash flows?
9.11 Consider the following investment cash flows:
Year Cash Flow
0 ($1,000)
1 250
2 400
3 500
4 600
5 600
a. What is the return expected on this investment measured in dollar terms if the opportunity cost rate is 10 percent?
b. Provide an explanation, in economic terms, of your answer.
c. What is the return on this investment measured in percentage terms?
d. Should this investment be made? Explain your answer.
10.1 Consider the following probability distribution of returns estimated for a proposed project that involves a new ultrasound machine:
State of Probability of the Economy Occurrence Rate of Return
Very poor 0.10-10.0 %
Poor 0.20 0.0
Average 0.40 10.0
Good 0.20 20.0
Very good 0.10 30.0
a. What is the expected rate of return on the project?
b. What is the project's standard deviation of returns?
c. What is the project's coefecient of variation (CV) of returns?
d. What type of risk does the standard deviation and CV measure?
e. In what situation is this risk relevant?
10.2 Suppose that a person won the Florida lottery and was offered a choice of two prizes: (1) $500,000 or (2) a coin-toss gamble in which he or she would get $1 million for heads and zero for a tail.
a. What is the expected dollar return on the gamble?
b. Would the person choose the sure $500,000 or the gamble?
c. If he or she chooses the sure $500,000, is the person a risk averter or a risk seeker?
10.5 A few years ago, the Value Line Investment Survey reported the following market betas for the stocks of selected healthcare providers:
Company Beta
Quorum Health Group 0.90
Beverly Enterprises 1.20
HEALTHSOUTH Corporation 1.45
United Healthcare 1.70
At the time these betas were developed, reasonable estimates for the risk-free rate, RF, and required rate of return on the market, R(RM), were 6.5 percent and 13.5 percent, respectively.
a. What are the required rates of return on the four stocks?
b. Why do their required rates of return differ?
c. Suppose that a person is planning to invest in only one stock rather than hold a well-diversified stock portfolio. Are the required rates of
return calculated above applicable to the investment? Explain your answer.
10.6 Suppose that Apex Health Services has four different projects. These projects are listed below, along with the amount of capital invested and estimated corporate and market betas:
Amount Corporate Market
Project Invested Beta Beta
Walk-in clinic $ 500,000 1.5 1.1
MRI facility 2,000,000 1.2 1.5
Clinical laboratory 1,500,000 0.9 0.8
X-ray laboratory 1,000,000 0.5 1.0
$5,000,000
a. Why do the corporate and market betas differ for the same project?
b. What is the overall corporate beta of Apex Health Services? Is the calculated beta consistent with corporate risk theory?
c. What is the overall market beta of Apex Health Services?
d. How does the riskiness of Apex's stock compare with the riskiness of an average stock?
e. Would stock investors require a rate of return on Apex that is greater than, less than, or the same as the return on an average-risk stock?
11.1 Assume Venture Healthcare sold bonds that have a ten-year maturity, a 12 percent coupon rate with annual payments, and a $1,000 par value.
a. Suppose that two years after the bonds were issued, the required interest rate fell to 7 percent. What would be the bond's value?
b. Suppose that two years after the bonds were issued, the required interest rate rose to 13 percent. What would be the bonds?? value?
c. What would be the value of the bonds three years after issue in each scenario above, assuming that interest rates stayed steady at either 7 percent or 13 percent?
11.2 Twin Oaks Health Center has a bond issue outstanding with a coupon rate of 7 percent and four years remaining until maturity. The par value of the bond is $1,000, and the bond pays interest annually.
a. Determine the current value of the bond if present market conditions justify a 14 percent required rate of return.
b. Now, suppose Twin Oaks four-year bond had semiannual coupon payments. What would be its current value? (Assume a 7 percent
semiannual required rate of return. However, the actual rate would be slightly less than 7 percent because a semiannual coupon bond is
slightly less risky than an annual coupon bond.)
c. Assume that Twin Oaks bond had a semiannual coupon but 20 years remaining to maturity. What is the current value under these
conditions? (Again, assume a 7 percent semiannual required rate of return, although the actual rate would probably be greater than 7
percent because of increased price risk.)
11.5 Minneapolis Health System has bonds outstanding that have four years remaining to maturity, a coupon interest rate of 9 percent paid
annually, and a $1,000 par value.
a. What is the yield to maturity on the issue if the current market price is $829?
b. If the current market price is $1,104?
c. Would you be willing to buy one of these bonds for $829 if you required a 12 percent rate of return on the issue? Explain your answer.
11.6 Six years ago, Bradford Community Hospital issued 20-year municipal bonds with a 7 percent annual coupon rate. The bonds were called today for a $70 call premium that is, bondholders received $1,070 for each bond. What is the realized rate of return for those investors who bought the bonds for $1,000 when they were issued?
12.1 A person is considering buying the stock of two home health companies that are similar in all respects except for the proportion of earnings paid out as dividends. Both companies are expected to earn $6 per share in the coming year, but Company D (for dividends) is expected to pay out the entire amount as dividends, while Company G (for growth) is expected to pay out only one-third of its earnings, or $2 per share.
The companies are equally risky, and their required rate of return is 15 percent. D's constant growth rate is zero and G's is 8.33 percent. What are the intrinsic values of Stocks D and G?
12.2 Medical Corporation of America (MCA) has a current stock price of $36 and its last dividend (D0) was $2.40. In view of MCA's strong
financial position, its required rate of return is 12 percent. If MCA's dividends are expected to grow at a constant rate in the future, what is
the firm's expected stock price in Five years?
12.3 A broker offers to sell you shares of Bay Area Healthcare, which just paid a dividend of $2 per share. The dividend is expected to grow at a constant rate of 5 percent per year. The stock's required rate of return is 12 percent.
a. What is the expected dollar dividend over the next three years?
b. What is the current value of the stock and the expected stock price at the end of each of the next three years?
c. What is the expected dividend yield and capital gains yield for each of the next three years?
d. What is the expected total return for each of the next three years?
E.How does the expected total return compare with the required rate of return on the stock? Does this make sense? Explain your answer.
12.7 Lucas Clinic's last dividend (D0) was $1.50. Its current equilibrium stock price is $15.75, and its expected growth rate is a constant 5percent. If the stockholder's required rate of return is 15 percent, what is the expected dividend yield and expected capital gains yield for the coming year?